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<H1 align="center">logP and logD Calculation</H1>
<OL>

<LI> <A HREF="#Intro">Introduction</A></LI>
<LI><A HREF="#Symbols">Symbols</A></LI>
<LI><A HREF="#logPD_Def">Definition of Partition Coefficient <i>P</i> and Distribution Coefficient <i>D</i></A></LI>
<LI><A HREF="#Microp">Micro Partition Coefficient</A></LI>
<LI><A HREF="#MacroMicroRel">Relation Between Macro and Micro Partition Coefficients</A></LI>
<li><a href="#methods">LogP calculation methods</a></li>
<LI><A HREF="#Examples">Examples</A></LI>


<UL>
<LI><A HREF="#Example1">Example 1</A></LI>
<LI><A HREF="#Example2">Example 2</A></LI>
<LI><A HREF="#Example3">Example 3</A></LI>
<LI><A HREF="#Example4">Example 4</A></LI>
</UL>


<LI><A HREF="#References">References</A></LI>

</OL>
<A NAME="Intro" ></A>
<H2>1. Introduction</H2>

The mass flux of a molecule at the interface of two immiscible solvents is governed by its lipophilicity. 
The more lipophilic a molecule is, the more soluble it is in lipophilic organic phase. 
For the same reason, drug penetration into a biological membrane is also influenced by its lipophilicity. 
When a molecule is ionizable at the pH of a solution, it forms a hydrophilic anion or cation and subsequently 
fails to dissolve in organic phase. Ionization of a molecule leads to the accumulation of the hydrophilic form
 in the aqueous phase. In contrast, its lipophilic form will decrease in both aqueous and organic phase 
 due to the law of conservation of mass. 
The partition coefficient of a molecule observed in a water&#8211;<i>n</i>-octanol system has been adopted as the standard measure of lipophilicity. 
The observed partition coefficient depends on the support electrolyte concentration of the bulk phase the compound is dissolved in. 
Extra ion-pair forming chemical agents added to the aqueous/organic phase may have a significant effect on the partitioning behavior of a molecule.
<BR>

It is often meaningful to obtain the partition coefficients of molecules by calculation.  
The molecular structure and extent of ionization are the primary factors in calculating the partition coefficient. 
The standard partition coefficient of ionized and unionized species calculated from the molecular structure is
based largely on the atomic log<i>P</i> increments given in <A HREF="#Ref1">Ref.1. </A>
The extent of ionization at a given pH is obtained from the predicted p<i>K</i><SUB>a</SUB> of a molecule.  
Our calculation method takes into account the effect of the counterion ion concentration on log<i>D</i> and log<i>P</i>.

<A NAME="Symbols"></A>
<H2>2. Symbols</H2>


Throughout this document we use the following symbols:
<ul>
<li><b><i>P</i><SUB>i</SUB></b> (upper case) the macro partition coefficient,
 where subscript i refers to the ionization state of species included in <i>P</i><SUB>i</SUB>. e.g. i= -2, -1, 0, +1, +2</li>
<li><b><i>p</i><SUB>i</SUB></b> (lower case) the micro partition coefficient,
 where subscript i refers to the microspecies. e.g. i=1,2,3,4,&hellip;</li>
<li><b><i>D</i></b> the distribution coefficient</li>
<li><b>[ ]</b> concentration of microspecies</li>
<li><b>log<i>P</i></b> the logarithm of the partition coefficient </li>
<li><b>log<i>D</i></b> the logarithm of the distribution coefficient</li>
</ul>


<H2><A class="anchor" NAME="logPD_Def">3. Definition of Partition Coefficient <i>P</i> and Distribution Coefficient <i>D</i></A></H2>

The partition coefficient is the ratio of the concentration of the compound in octanol to the concentration of the compound in water.
The distribution coefficient is the ratio of the sum of the concentrations of all species of the 
compound in octanol to the sum of the concentrations of all species of the compound in water.

Based on acid dissociation reactions, we can introduce the concept of a partition coefficient 
for cationic and anionic species and for neutral species. 
The following gives the definition of partition and distribution coefficients 
for ionized and unionized species.

<BR><img src="logPlogD_files/logPlogD_def.png" width="686" height="313" alt="logPlogD_def"/>

<BR>

The partition and distribution coefficients for multiprotic compounds are defined in much the same way as for monoprotic compounds, using the following formulas.


<BR><img src="logPlogD_files/multipro_def.png" width="679" height="233" alt="multipro_def"/>
<BR>

<H3><A class="anchor" NAME="Example">Example</A></H3>

In this example we suppose that the compound A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB> contains two acidic and two basic ionization sites.
This compound has 16 protonation states in aqueous solution. The microspecies which are assigned to the protonation states 
are summarized in Table 1.
<BR>
<BR>Table 1. 
<TABLE BORDER=1 WIDTH=40% HEIGHT=25% cellpadding="0" cellspacing="1" >

<TR><TD ><CENTER>Microspecies</CENTER></TD>
<TD><CENTER>charge</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB></CENTER></TD>
<TD><CENTER>0</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB><SUP>-</SUP>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB></CENTER></TD>
<TD><CENTER>-1</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB>A<SUB>2</SUB><SUP>-</SUP>B<SUB>1</SUB>B<SUB>2</SUB></CENTER></TD>
<TD><CENTER>-1</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB><SUP>+</SUP>B<SUB>2</SUB></CENTER></TD>
<TD><CENTER>+1</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB><SUP>+</SUP></CENTER></TD>
<TD><CENTER>+1</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB><SUP>-</SUP>A<SUB>2</SUB><SUP>-</SUP>B<SUB>1</SUB>B<SUB>2</SUB></CENTER></TD>
<TD><CENTER>-2</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB><SUP>-</SUP>A<SUB>2</SUB>B<SUB>1</SUB><SUP>+</SUP>B<SUB>2</SUB></CENTER></TD>
<TD><CENTER>0</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB><SUP>-</SUP>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB><SUP>+</SUP></CENTER></TD>
<TD><CENTER>0</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB>A<SUB>2</SUB><SUP>-</SUP>B<SUB>1</SUB><SUP>+</SUP>B<SUB>2</SUB></CENTER></TD>
<TD><CENTER>0</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB>A<SUB>2</SUB><SUP>-</SUP>B<SUB>1</SUB>B<SUB>2</SUB><SUP>+</SUP></CENTER></TD>
<TD><CENTER>0</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB><SUP>+</SUP>B<SUB>2</SUB><SUP>+</SUP></CENTER></TD>
<TD><CENTER>+2</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB><SUP>-</SUP>A<SUB>2</SUB><SUP>-</SUP>B<SUB>1</SUB><SUP>+</SUP>B<SUB>2</SUB></CENTER></TD>
<TD><CENTER>-1</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB><SUP>-</SUP>A<SUB>2</SUB><SUP>-</SUP>B<SUB>1</SUB>B<SUB>2</SUB><SUP>+</SUP></CENTER></TD>
<TD><CENTER>-1</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB><SUP>-</SUP>A<SUB>2</SUB>B<SUB>1</SUB><SUP>+</SUP>B<SUB>2</SUB><SUP>+</SUP></CENTER></TD>
<TD><CENTER>+1</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB>A<SUB>2</SUB><SUP>-</SUP>B<SUB>1</SUB><SUP>+</SUP>B<SUB>2</SUB><SUP>+</SUP></CENTER></TD>
<TD><CENTER>+1</CENTER></TD>

<TR><TD><CENTER>A<SUB>1</SUB><SUP>-</SUP>A<SUB>2</SUB><SUP>-</SUP>B<SUB>1</SUB><SUP>+</SUP>B<SUB>2</SUB><SUP>+</SUP></CENTER></TD>
<TD><CENTER>0</CENTER></TD>

</TABLE>

<BR>
Partition coefficients and distribution coefficients are expressed by the following formulas: 
<table border="0">
  <tbody>
<tr><td>1. Partition coefficient of the neutral species:</td>
<td colspan="2">
<img src="logPlogD_files/P0_exp.png" width="738" height="100" alt="P0_exp"/>
</td></tr>
<tr><td>
2. Partition coefficient of the anionic and the cationic species:</td>
<td>
<img src="logPlogD_files/P_ion1_exp.png" width="543" height="153" alt="P_ion1_exp"/>
</td>
<td colspan="2">
<img src="logPlogD_files/P_ion2_exp.png" width="233" height="154" alt="P_ion2_exp"/>
</td><td></td></tr>

<tr><td>3. The distribution coefficient of the A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB> molecule:</td>
<td><img src="logPlogD_files/D_exp.png" width="297" height="89" alt="D_exp"/></td></tr>
</tbody>
</table>


<H2><A class="anchor" NAME="Microp">4. Micro Partition Coefficient</A></H2>

The micro partition coefficient is the ratio of the concentration of two microspecies defined with <i>p</i><SUB>i</SUB> 
as expressed with the next relation:
<BR><img src="logPlogD_files/pi_exp.png" width="236" height="66" alt="pi_exp"/>


<BR>


<H2><A class="anchor" NAME="MacroMicroRel">5. Relation Between Macro and Micro Partition Coefficients</A></H2>

Macro partition coefficients<i> P<SUB>0</SUB>&hellip;P<SUB>i</SUB></i> 
can also be expressed as a function of micro partition coefficients <i>p<SUB>0</SUB>&hellip;p<SUB>i</SUB></i>.

<BR>From the definition of micro partition coefficients, we obtain the following formula for the concentration of microspecies in octanol:
<BR>
<BR>[microspecies]<SUB>i,octanol</SUB> =<i> p</i><SUB>i</SUB> &sdot;[microspecies]<SUB>i,water</SUB>
<BR>
where <i>p</i><SUB>i</SUB> is the micro partition coefficient of microspecies i. 
<BR>
<BR>For example, <i> P</i><SUB>-1</SUB> includes four micro partition coefficients 
(<i>p<SUB>1</SUB>, p<SUB>2</SUB>, p<SUB>3</SUB>, p<SUB>4</SUB></i>).
They are given by:
<p><img src="logPlogD_files/p1p2p3p4.png" width="433" height="155" alt="p1p2p3p4"/></p>

<p>

After substituting the <i>p</i><SUB>i</SUB>s  into the original formula for <i>P</i><SUB>-1</SUB> 
we get the following simpler formula which includes only aqueous concentration of the 
appropriate microspecies:</p>
<p><img src="logPlogD_files/P_1_new.png" width="801" height="89" alt="P_1_new"/>
<p>
This can be further simplified if we introduce the acid dissociation constants of the 
A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB> molecule.
The next five ionization reactions of the A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB>
molecule are used to rearrange <i>P</i><SUB>-1</SUB> into a concentration free form.
<p><img src="logPlogD_files/5_reaction.png" width="529" height="380" alt="5_reaction"/>

</p>
So we can further simplify the formula for <i>P</i><SUB>-1</SUB> to the following.  
 This expression reveals that <i>P</i><SUB>-1</SUB> does not depend on the pH of the solution: 
 <BR><img src="logPlogD_files/P_1_Concfree.png" width="367" height="115" alt="P_1_Concfree"/>
<BR>
 <BR>
 Similarly, one could show that 
  <i>P</i><SUB>0</SUB>, <i>P</i><SUB>+1</SUB>,<i> P</i><SUB>-2</SUB> 
 and <i>P</i><SUB>+2</SUB> are also pH-independent.<BR>
<BR>
In contrast to this, the distribution coefficient <i>D</i> does depend on the solution 
pH (see <A HREF="#Ref2">Ref.2.</A>):

<BR><img src="logPlogD_files/D_pi.png" width="318" height="80" alt="D_pi"/>
<br>
  
<h2><a class="anchor" name="methods">6. log<i>P</i> calculation methods</a></h2>
<p><table>
    <tr><td><p>log<i>P</i> calculations are based on a pool of fragments predefined
    in the calculator. This set is based on the data set in <a href="#Ref1"> 
    references 1</a>. Every fragment is assigned a unique name and a value. <br>
      </td>
      <!--<td><img src="logPlogD_files/set1.png" width="237" height="247" alt="set1"/>
    </td>--></tr>
    
    <tr><td>
        The log<i>P</i> value of a molecule
        is the sum of the fragment values present in the molecule. <br>
      </td>
    <!--  <td><img src="logPlogD_files/fragments.png" width="417" height="514" alt="fragments"/>
    </td>--></tr>
    
    <tr><td>
        log<i>P</i> plugin handled 
        only one fragment set until version 5.1.2, above, it was extended with two additional 
        sets. The sets are based on a published data set (see <a href="#Ref1a"> 
        reference 2</a>) and the PhysProp<sup>&copy;</sup> database.<br>
      </td>
      <!--<td><img src="logPlogD_files/allsets.png" width="477" height="259" alt="allsets"/>
    </td>--></tr>
    
    
    <tr><td>The <b>trainable log<i>P</i></b> (available from version 5.1.3) offers the user to define 
        his own log<i>P</i> database and calculate log<i>P</i> values based on the experimental data. 
        New fragment value extensions make a more precise calculation possible. <br>
      </td>
      
      <!--<td><img src="logPlogD_files/userset.png" width="771" height="423" alt="userset"/>
    </td>--></tr>
    <tr>
      <td>Choosing the weighted method requires the user to define the weight of each 
        set of data needed. This method may include any of the three internal data sets and 
        the user defined set.<br>
        
      </td>
      <!--<td><img src="logPlogD_files/weighted.png" width="939" height="616" alt="weighted"/>
    </td>--></tr>
  </table>
 </p>
 <br>
   
 <H2><A class="anchor" NAME="Examples">7. Examples</A> </H2>

<h3><A class="anchor" NAME="Example1">Example 1</A></h3>
The compound below is zwitterionic that looks like 
the A<SUB>1</SUB>A<SUB>2</SUB>B<SUB>1</SUB>B<SUB>2</SUB> molecule in the theoretical section above. Lipophilicity of this compound reaches its maximum near to the isoelectric point.
<table>
<tr><td><IMG SRC="logPlogD_files/mol_logD-pH.png"  width="298" height="268"   HSPACE=18 VSPACE=10 ></td>
<td><IMG SRC="logPlogD_files/logD-pH.jpg" width="556" height="417"  HSPACE=18 VSPACE=10 ></td> 
</tr>
</table>

<h3><A class="anchor" NAME="Example2">Example 2</a></h3>
Homidium is a quaternary ammonium ion with strong hydrophilic character. 
Its log<i>P</i> is calculated with the use of the ionic fragment of the N<SUP>+</SUP> ion.
The calculated and measured log<i>P</i> agree.
<BR>
<table border=0 cellpadding=5 cellspacing=5>
<tr>
<td>
Calculated log<i>P</i> = -1.09 </td>
<td> measured log<i>P</i>= -1.10 </td>
<td>
, see <A HREF="#Ref3">Ref.3.</A></td>
</tr>
</table>
<BR>
<IMG SRC="logPlogD_files/homidium.png"     HSPACE=18 VSPACE=10 > 


<h3><A class="anchor" NAME="Example3"></a>Example 3</h3>
Ibuprofen has the typical log<i>D</i> vs. pH profile that is characteristic of acidic compounds. 
Lipophilic behavior of ibuprofen will be dominant when its carboxylic group is unionized (at low pH). 
At higher pH the carboxylic group reaches the fully ionized state and hydrofilicity becomes enhanced. 
<BR>

<IMG SRC="logPlogD_files/ibuprofen_logD.jpg"   HSPACE=18 VSPACE=10 > 


<h3><A class="anchor" NAME="Example4"></a>Example 4</h3>
The measured distribution coefficient also depends on the method.  
The shake flask and the pH-metric methods are the most popular. 
The figure below shows the calculated and measured log<i>D</i> of 
lignocaine as function of pH. 
<BR>

<IMG SRC="logPlogD_files/lignocaine_logD.jpg"  HSPACE=6 VSPACE=10 > 
<BR clear=LEFT>
<P>&nbsp;<P>

<H2><A class="anchor" NAME="References"></a>7. References</H2>
<OL>

<LI><A class="text" NAME="Ref1">Viswanadhan, V. N.; Ghose, A. K.; Revankar, G. R. and Robins, R. K., <i> J.Chem.Inf.Comput.Sci.</i>, <b>1989</b>, <i>29</i>, 3, 163-172; <a href="http://dx.doi.org/10.1021/ci00063a006">doi</a></A></LI>
<li><a class="text" name="Ref1a">Klopman, G.; Li, Ju-Yun.; Wang, S.; Dimayuga,  M.: <i>J.Chem.Inf.Comput.Sci.</i>, <b>1994</b>, <i>34</i>, 752; <a href="http://dx.doi.org/10.1021/ci00020a009">doi</a></a></li>
<li>PhysProp<sup>&copy;</sup> database, <a href="http://esc.syrres.com/interkow/pp1357.htm">webpage</a></li>
<LI><A class="text" NAME="Ref2">Csizmadia, F.; Tsantili-Kakoulidou, A.; Panderi, I. and Darvas, F., <i>J.Pharm.Sci.</i>, <b>1997</b>, <i>86</i>, 7, 865-871; <a href="http://dx.doi.org/10.1021/js960177k">doi</a></A></LI>
<LI><A class="text" NAME="Ref3">Bouchard, G.; Carrupt, P. A.; Testa, B.; Gobry, V. and Girault, H. H., <i>Pharm.Res.</i>, <b>2001</b>, <i>18</i>, 5, 702-708; <a href="http://dx.doi.org/10.1023/A:1011001914685">doi</a></A></LI>

</OL>

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